Question

A source of sound of frequency 256 Hz is moving rapidly towards a wall with a velocity of 5 m/s (sound travels at a speed of 330 m/s) Among the following choose the wrong statement.

• A. If the observer is in between the source and the wall he hears no beats
• B. If the source is between the observer and the reflecting surface he hears beats at the frequency of 7.7 Hz
• C. If the observer and the source are moving towards the wall, he hears beats at the frequency of 7.9 Hz
• D. If the observer is in between the source and the wall he hears beats at the frequency of 7.7 Hz

Answer 1

The correct option is D If the observer is in between the source and the wall he hears beats at the frequency of 7.7 Hz

Source and observer

$f^{{}^{\prime }}=256\left(\frac{330-0}{330+5}\right)=252.18Hz$

Observer and echo

$f^{{}^{\prime \prime }}=256\left(\frac{330-0}{330+5}\right)=252.18Hz$

$\therefore$ In this case he hears no beats.

$\therefore f^{{}^{\prime \prime }}-f^{{}^{\prime }}=0$

APPROACH : In this kind of questions where 2 options given for a same case, one has to be correct and other has to be wrong. Here, Case in $\left[A\right]$ and

$\left[D\right]$ is same, therefore we checked out this case first. No need to check other options in sign correct multiple question.